The DM \(H^0\)  in this low mass region could be constrained by the DM direct detection experiments. Since we need a relatively large Higgs-mediation annihilation channel to generate DM relic abundance, the Higgs exchange channel can also give rise to sizeable spin-independent signals, with the corresponding DM-nucleon cross section as follows [1]}:
\(\sigma _{H^0 N}={m_r^2\over 4\pi }\Big ({\lambda _L\over M_H M_h^2}\Big )^2f^2m_N^2\;.\) 
